Affiliation:
1. Chongqing Institute of Engineering
Abstract
Abstract
The minimum set covering problem with a wide application background is a classical NP problem in the combinatorial optimization and theoretical computing, which defect is at exponential time complexity. Therefore, based on the compatible relations in set theory，this paper constructed the minimum set cover search model, designed an exact algorithm (MSCPT) to solve the minimum set cover on the maximum simple cover, and conducted its time complexity analysis, proof and time performance test. Finally, MSCPT is applied to the optimal location of express service points. The test results show that the MSCPT with sub exponential time complexity can effectively solve the exact solution in small-scale set cover, and its practical application is simple, feasible and steady.
Publisher
Research Square Platform LLC
Reference32 articles.
1. Michael R Garey.Computers and Intractability - A Guide to the Theory of NP - Completeness[M]. Calif: W.H.Freeman & Co.,San Francisco,1979:71.
2. Reduced Order Backtracking Algorithm for Covering Location Problem with Capacity Set[J];Shang Chunjian Ning;Journal of Chinese Computer Systems,2020
3. Karp R.M. Reducibility Among Combinatorial Problems[J]. Complexity of Computer Computations, Plenum Press, New York, 1972:85–103.
4. A Tight Analysis of the Greedy Algorithm for Set Cover[J];Petr Slavik;Journal of Algorithms,1997
5. A Threshold of ln(n) for Approximating Set Cover[J];Uriel Feige;Journal of the ACM,1998